Alvaro Morata grabbed a hat-trick as Chelsea earned a fourth win in five unbeaten Premier League matches.
Morata scored inside two minutes after a fabulous pass by stand-in captain Cesar Azpilicueta and Pedro made it 2-0 by the interval with a powerful shot into the far corner.
Stoke piled on the pressure after the break, but the Blues stood firm and made the game safe in the closing stages.
Morata ran from the half-way line and beat Darren Fletcher before dinking a delightful third goal over goalkeeper Jack Butland.
And the fourth goal was also made in Spain, Azpilicueta chesting the ball to Morata to slide in his hat-trick after a sumptuous pass by substitute Cesc Fabregas.
Stoke only managed two efforts on target throughout but had plenty of possession and looked increasingly dangerous after the interval as they looked to play a more direct style.
Morata’s second-minute opener came after Tiemoue Bakayoko and N’Golo Kante combined to find Azpilicueta, whose ball over the top into the right channel allowed the Blues striker to run through, take one touch and then place the ball into the far corner.
A mistake by Darren Fletcher contributed to Chelsea’s second goal. The former Manchester United midfielder chested the ball back towards his own goal and the ever-alert Pedro latched onto the mistake and smashed the ball into the far corner.
The impressive Xherdan Shaqiri posed the home side’s biggest threat, sending in dangerous free-kicks that could have led to goals for Joe Allen, Mame Diouf and substitute Peter Crouch.
But Morata’s delightful run and finish made the game safe and he sealed his treble from two yards after another brilliant Azpilicueta assist.
Morata could have ended up with five goals, firing one effort narrowly wide and getting his feet in a mess from the goalline from a blasted Victor Moses cross-shot.
Chelsea: Courtois; Azpilicueta, Christensen, Rudiger; Moses, Kante, Bakayoko, Alonso (Cahill 59); Willian (Hazard 72), Morata, Pedro (Fabregas 68).
Subs not used: Caballero, Zappacosta, Musonda, Batshuayi.